A key requirement of lunar rover autonomous navigation is to acquire state information accurately in real-time during its motion and set up a gradual parameter-based nonlinear kinematics model for the rover. In this paper, we propose a dual-extended-Kalman-filter- dual-EKF- based real-time celestial navigation RCN method. The proposed method considers the rover position and velocity on the lunar surface as the system parameters and establishes a constant velocity CV model. In addition, the attitude quaternion is considered as the system state, and the quaternion differential equation is established as the state equation, which incorporates the output of angular rate gyroscope. Therefore, the measurement equation can be established with sun direction vector from the sun sensor and speed observation from the speedometer. The gyro continuous output ensures the algorithm real-time operation. Finally, we use the dual-EKF method to solve the system equations. Simulation results show that the proposed method can acquire the rover position and heading information in real time and greatly improve the navigation accuracy. Our method overcomes the disadvantage of the cumulative error in inertial navigation.